Achieving Spatial Adaptation via Inconstant Penalization: Theory and Computational Strategies

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

The investigator will study the relation between inconstant penalization and local adaptivity. The goal is to achieve location adaptive functional estimation when the underlying model (of the relation between a response and input variables) has inhomogeneous roughness. The investigator will (1) quantify the connection between a variable penalty function and the resulting local adaptivity, (2) generalize the methods for high-dimensional input variables, (3) study the selection of algorithmic parameters, (4) derive theoretical properties of the resulting estimators, and (5) design fast computational strategies. Functional estimation under inhomogeneous roughness is a fundamental problem in many statistical applications. This study will contribute to the fundamental understanding to these problems, as well as providing deployable tools. Especially for large size datasets, better performance than the current state-of-the-art methodology is anticipated.